It is a well known principle of dynamics that the inertia of a circular body can be determined by applying a known rotational force to the body and measuring the rotational distance traveled by the body, over a fixed period of time. What is new is that this principle of dynamics can be used to determine the amount of magnetic tape placed on a reel enclosed in a cartridge.
The rotational force/acceleration relationship is that the angular acceleration is equal to the torque divided by the rotational inertia. If the rotational body is assumed to be initially at rest and the amount of rotational force is constant with regard to time, then the amount of torque applied to a rotational body will impart a fixed displacement over a fixed period of time. The angular acceleration of different inertias of the different bodies is different, this different angular acceleration will result in different distances traveled by the body during the reference period of time. Therefore, the rotational distance traveled during the application of the torque is in inverse proportion to the inertia of the rotated body.